This script examines whether the vocabulary and grammar sections of the CDI can be distinguished as separate dimensions1.

Open the libraries.

options(max.print=500)
library(wordbankr) # WB data
library(tidyverse) # tidy
library(mirt) # IRT models
library(psych) # some psychometric stuff (tests of dimensionality)
library(Gifi)# some more psychometric stuff (tests of dimensionality)
library(knitr) # some formatting, tables, etc
library(lordif) # differential item functioning.
library(sirt) # additional IRT functions

1 Data Preparation

Inst <- get_instrument_data(language="English (American)", form="WS")
Admin <- get_administration_data(language="English (American)", form="WS")
N_total = nrow(Admin) # making sure things add up later
N_long = nrow(filter(Admin, longitudinal==TRUE)) # making sure things add up later
Item <- get_item_data(language="English (American)", form = "WS")

1.1 Make Complexity Data

Complex <- Admin %>%
  full_join(.,Inst, by="data_id") %>%
  full_join(., Item, by="num_item_id") %>%
  filter(longitudinal==FALSE) %>%
  filter(type == "combine" | # to drop non-combiners
           type == "complexity" # to calculate complexity scores.
         ) %>%
  mutate(
    out = ifelse(value=="complex" | value=="sometimes" | value=="produces", yes=1, 
                 no = ifelse(value=="often", yes=2, no =0))
  ) 

N_complexity_items = nrow(filter(Item, type == "combine" | 
           type == "complexity"))

nrow(Complex) == (N_total - N_long)*N_complexity_items
## [1] TRUE
Complex$complexity_category <- ifelse(Complex$complexity_category == "", yes=Complex$type, no=Complex$complexity_category)
Complex_short_with_ids_all <- Complex %>% 
  dplyr::select(data_id, value, out, complexity_category, num_item_id) %>%
  mutate(
    label = str_c(complexity_category, num_item_id)
  ) %>%
  pivot_wider(id_cols=data_id, names_from = "label", values_from="out") %>%
  dplyr::select(starts_with(c("data_id", "combine", "morphology", "syntax"))) 

Complex_short_with_ids <- Complex_short_with_ids_all %>%  
drop_na()

N_NA <- nrow(Complex_short_with_ids_all) - nrow(Complex_short_with_ids)

Complex_short_grammatical <- Complex_short_with_ids %>%
  filter(combine760 > 0) %>%
  dplyr::select(starts_with(c("morphology", "syntax"))) # need to get rid of participant names for IRT models. 

N_nog <- nrow(filter(Complex_short_with_ids, combine760 == 0))

nrow(Complex_short_grammatical) == N_total - N_long - N_NA - N_nog
## [1] TRUE

1.2 Make Vocab Dataset

Vocab <- Admin %>%
  full_join(.,Inst, by="data_id") %>%
  full_join(., Item, by="num_item_id") %>%
  filter(longitudinal==FALSE) %>% # remove longitudinal data set
  filter(type == "word"
         ) %>%
  mutate(
    out = ifelse(value=="produces", yes=1, no =0)
    )

N_vocab = nrow(filter(Item, type == "word")) 

nrow(Vocab) == (N_total - N_long)*N_vocab
## [1] TRUE
Vocab_short_with_ids_all <- Vocab %>% 
  filter(lexical_category == "nouns" | lexical_category == "predicates") %>%
  dplyr::select(data_id, value, out, definition) %>%
  pivot_wider(id_cols=data_id, names_from = "definition", values_from="out") 

Vocab_short_with_ids <- Vocab_short_with_ids_all %>%  
  drop_na() # drop participants with missing data

N_NA_Vocab = nrow(Vocab_short_with_ids_all) - nrow(Vocab_short_with_ids)

Vocab_short <- Vocab_short_with_ids %>%
  dplyr::select(-"data_id") # dataset for IRT can't have IDs

nrow(Vocab_short_with_ids) == N_total - N_long - N_NA_Vocab # Looks good
## [1] TRUE

##Combine

full <- full_join(
  Complex_short_with_ids, Vocab_short_with_ids, by="data_id"
) %>%
  filter(combine760 > 0) %>%
  dplyr::select(-c("data_id", "combine760")) %>%
  drop_na() # one participant with missing vocab, but full grammar. 

2 Some quick checks of dimensionality.

full_tetra <- tetrachoric(full)
## For i = 147 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 153 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 168 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 177 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 177 j = 96  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 177 j = 113  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 177 j = 124  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 197 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 203 j = 113  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 203 j = 146  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 203 j = 150  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 205 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 206 j = 124  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 227 j = 203  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 230 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 235 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 262 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 291 j = 226  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 291 j = 289  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 321 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 424 j = 95  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 485 j = 482  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## For i = 496 j = 482  A cell entry of 0 was replaced with correct =  0.5.  Check your data!
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was done
rho <- full_tetra$rho
fa.parallel(rho, fa="fa", fm="minres", cor="poly", n.obs = 2187)
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Parallel analysis suggests that the number of factors =  22  and the number of components =  NA
vss(rho, fa="fa", fm="minres", cor="poly", n.obs = 2187)
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## 
## Very Simple Structure
## Call: vss(x = rho, fm = "minres", n.obs = 2187, cor = "poly", fa = "fa")
## VSS complexity 1 achieves a maximimum of 1  with  1  factors
## VSS complexity 2 achieves a maximimum of 1  with  2  factors
## 
## The Velicer MAP achieves a minimum of 0  with  8  factors 
## BIC achieves a minimum of  -719118.7  with  8  factors
## Sample Size adjusted BIC achieves a minimum of  -311609.2  with  8  factors
## 
## Statistics by number of factors 
##   vss1 vss2    map    dof  chisq prob sqresid fit RMSEA     BIC   SABIC complex
## 1 1.00 0.00 0.0103 131840 991350    0     493   1 0.055  -22537  396337     1.0
## 2 0.47 1.00 0.0066 131326 605072    0     301   1 0.041 -404863   12378     1.8
## 3 0.35 0.84 0.0056 130813 487647    0     242   1 0.035 -518342 -102731     2.4
## 4 0.29 0.72 0.0049 130301 405258    0     202   1 0.031 -596794 -182810     2.9
## 5 0.27 0.70 0.0041 129790 339688    0     169   1 0.027 -658435 -246074     3.1
## 6 0.28 0.72 0.0039 129280 309960    0     154   1 0.025 -684240 -273500     3.2
## 7 0.28 0.72 0.0037 128771 287944    0     143   1 0.024 -702342 -293219     3.3
## 8 0.28 0.72 0.0035 128263 267261    0     133   1 0.022 -719119 -311609     3.3
##   eChisq  SRMR eCRMS    eBIC
## 1 901585 0.039 0.040 -112302
## 2 504995 0.030 0.030 -504939
## 3 389686 0.026 0.026 -616304
## 4 309520 0.023 0.023 -692532
## 5 246391 0.021 0.021 -751732
## 6 219575 0.019 0.020 -774625
## 7 200639 0.019 0.019 -789647
## 8 182481 0.018 0.018 -803898

3 Try MIRT model.

m1 <- mirt(full, 1, "2PL")
## 
Iteration: 1, Log-Lik: -431726.127, Max-Change: 2.47582
Iteration: 2, Log-Lik: -413209.854, Max-Change: 0.62342
Iteration: 3, Log-Lik: -411852.805, Max-Change: 0.41947
Iteration: 4, Log-Lik: -411617.221, Max-Change: 0.39023
Iteration: 5, Log-Lik: -411311.595, Max-Change: 0.16290
Iteration: 6, Log-Lik: -411085.937, Max-Change: 0.09963
Iteration: 7, Log-Lik: -410913.493, Max-Change: 0.04408
Iteration: 8, Log-Lik: -410771.139, Max-Change: 0.03733
Iteration: 9, Log-Lik: -410644.852, Max-Change: 0.03910
Iteration: 10, Log-Lik: -410539.751, Max-Change: 0.03341
Iteration: 11, Log-Lik: -410440.300, Max-Change: 0.03284
Iteration: 12, Log-Lik: -410348.890, Max-Change: 0.03135
Iteration: 13, Log-Lik: -410265.164, Max-Change: 0.03150
Iteration: 14, Log-Lik: -410187.664, Max-Change: 0.02975
Iteration: 15, Log-Lik: -410116.135, Max-Change: 0.03033
Iteration: 16, Log-Lik: -410049.432, Max-Change: 0.02937
Iteration: 17, Log-Lik: -409988.094, Max-Change: 0.02833
Iteration: 18, Log-Lik: -409931.110, Max-Change: 0.02717
Iteration: 19, Log-Lik: -409878.502, Max-Change: 0.02656
Iteration: 20, Log-Lik: -409829.547, Max-Change: 0.03697
Iteration: 21, Log-Lik: -409787.684, Max-Change: 0.06665
Iteration: 22, Log-Lik: -409747.543, Max-Change: 0.04088
Iteration: 23, Log-Lik: -409712.692, Max-Change: 0.05191
Iteration: 24, Log-Lik: -409676.834, Max-Change: 0.03679
Iteration: 25, Log-Lik: -409638.532, Max-Change: 0.02540
Iteration: 26, Log-Lik: -409602.667, Max-Change: 0.02379
Iteration: 27, Log-Lik: -409568.840, Max-Change: 0.02311
Iteration: 28, Log-Lik: -409537.078, Max-Change: 0.04110
Iteration: 29, Log-Lik: -409509.755, Max-Change: 0.08295
Iteration: 30, Log-Lik: -409485.716, Max-Change: 0.09534
Iteration: 31, Log-Lik: -409464.490, Max-Change: 0.12987
Iteration: 32, Log-Lik: -409443.700, Max-Change: 0.14632
Iteration: 33, Log-Lik: -409425.085, Max-Change: 0.17484
Iteration: 34, Log-Lik: -409406.856, Max-Change: 0.20722
Iteration: 35, Log-Lik: -409390.436, Max-Change: 0.21880
Iteration: 36, Log-Lik: -409374.433, Max-Change: 0.22359
Iteration: 37, Log-Lik: -409359.626, Max-Change: 0.27153
Iteration: 38, Log-Lik: -409345.093, Max-Change: 0.15973
Iteration: 39, Log-Lik: -409326.637, Max-Change: 0.01647
Iteration: 40, Log-Lik: -409309.733, Max-Change: 0.05400
Iteration: 41, Log-Lik: -409293.719, Max-Change: 0.13653
Iteration: 42, Log-Lik: -409279.975, Max-Change: 0.22528
Iteration: 43, Log-Lik: -409267.621, Max-Change: 0.28774
Iteration: 44, Log-Lik: -409255.569, Max-Change: 0.32913
Iteration: 45, Log-Lik: -409243.921, Max-Change: 0.29623
Iteration: 46, Log-Lik: -409232.459, Max-Change: 0.29597
Iteration: 47, Log-Lik: -409221.311, Max-Change: 0.29101
Iteration: 48, Log-Lik: -409210.617, Max-Change: 0.28325
Iteration: 49, Log-Lik: -409200.200, Max-Change: 0.25655
Iteration: 50, Log-Lik: -409190.199, Max-Change: 0.23962
Iteration: 51, Log-Lik: -409180.542, Max-Change: 0.26149
Iteration: 52, Log-Lik: -409171.442, Max-Change: 0.27319
Iteration: 53, Log-Lik: -409162.733, Max-Change: 0.28434
Iteration: 54, Log-Lik: -409154.517, Max-Change: 0.28962
Iteration: 55, Log-Lik: -409146.702, Max-Change: 0.29790
Iteration: 56, Log-Lik: -409139.388, Max-Change: 0.29554
Iteration: 57, Log-Lik: -409132.454, Max-Change: 0.33503
Iteration: 58, Log-Lik: -409125.087, Max-Change: 0.28257
Iteration: 59, Log-Lik: -409118.403, Max-Change: 0.28574
Iteration: 60, Log-Lik: -409111.625, Max-Change: 0.31758
Iteration: 61, Log-Lik: -409105.564, Max-Change: 0.15891
Iteration: 62, Log-Lik: -409098.397, Max-Change: 0.08739
Iteration: 63, Log-Lik: -409092.202, Max-Change: 0.22700
Iteration: 64, Log-Lik: -409086.963, Max-Change: 0.20162
Iteration: 65, Log-Lik: -409080.961, Max-Change: 0.17782
Iteration: 66, Log-Lik: -409076.200, Max-Change: 0.12593
Iteration: 67, Log-Lik: -409070.822, Max-Change: 0.03162
Iteration: 68, Log-Lik: -409066.044, Max-Change: 0.10040
Iteration: 69, Log-Lik: -409061.648, Max-Change: 0.13978
Iteration: 70, Log-Lik: -409056.650, Max-Change: 0.14577
Iteration: 71, Log-Lik: -409052.768, Max-Change: 0.21247
Iteration: 72, Log-Lik: -409049.204, Max-Change: 0.19430
Iteration: 73, Log-Lik: -409047.256, Max-Change: 0.01077
Iteration: 74, Log-Lik: -409043.414, Max-Change: 0.02041
Iteration: 75, Log-Lik: -409039.850, Max-Change: 0.01494
Iteration: 76, Log-Lik: -409035.024, Max-Change: 0.01603
Iteration: 77, Log-Lik: -409031.682, Max-Change: 0.01025
Iteration: 78, Log-Lik: -409028.564, Max-Change: 0.01575
Iteration: 79, Log-Lik: -409021.302, Max-Change: 0.09140
Iteration: 80, Log-Lik: -409018.381, Max-Change: 0.10997
Iteration: 81, Log-Lik: -409016.296, Max-Change: 0.10970
Iteration: 82, Log-Lik: -409015.012, Max-Change: 0.00944
Iteration: 83, Log-Lik: -409012.578, Max-Change: 0.01009
Iteration: 84, Log-Lik: -409010.334, Max-Change: 0.02111
Iteration: 85, Log-Lik: -409005.597, Max-Change: 0.10325
Iteration: 86, Log-Lik: -409003.694, Max-Change: 0.10124
Iteration: 87, Log-Lik: -409002.181, Max-Change: 0.09242
Iteration: 88, Log-Lik: -409001.298, Max-Change: 0.00782
Iteration: 89, Log-Lik: -408999.525, Max-Change: 0.00820
Iteration: 90, Log-Lik: -408997.845, Max-Change: 0.00673
Iteration: 91, Log-Lik: -408994.453, Max-Change: 0.00685
Iteration: 92, Log-Lik: -408992.821, Max-Change: 0.00693
Iteration: 93, Log-Lik: -408991.499, Max-Change: 0.00654
Iteration: 94, Log-Lik: -408987.322, Max-Change: 0.01789
Iteration: 95, Log-Lik: -408986.119, Max-Change: 0.00549
Iteration: 96, Log-Lik: -408985.135, Max-Change: 0.00635
Iteration: 97, Log-Lik: -408982.201, Max-Change: 0.01402
Iteration: 98, Log-Lik: -408981.365, Max-Change: 0.00501
Iteration: 99, Log-Lik: -408980.632, Max-Change: 0.00372
Iteration: 100, Log-Lik: -408978.528, Max-Change: 0.00394
Iteration: 101, Log-Lik: -408977.959, Max-Change: 0.00422
Iteration: 102, Log-Lik: -408977.436, Max-Change: 0.00324
Iteration: 103, Log-Lik: -408975.546, Max-Change: 0.00391
Iteration: 104, Log-Lik: -408975.133, Max-Change: 0.00273
Iteration: 105, Log-Lik: -408974.783, Max-Change: 0.00339
Iteration: 106, Log-Lik: -408973.348, Max-Change: 0.00372
Iteration: 107, Log-Lik: -408973.069, Max-Change: 0.01024
Iteration: 108, Log-Lik: -408972.772, Max-Change: 0.00268
Iteration: 109, Log-Lik: -408972.236, Max-Change: 0.00641
Iteration: 110, Log-Lik: -408972.076, Max-Change: 0.00529
Iteration: 111, Log-Lik: -408971.870, Max-Change: 0.00225
Iteration: 112, Log-Lik: -408971.397, Max-Change: 0.00439
Iteration: 113, Log-Lik: -408971.222, Max-Change: 0.00219
Iteration: 114, Log-Lik: -408971.024, Max-Change: 0.00256
Iteration: 115, Log-Lik: -408970.781, Max-Change: 0.00127
Iteration: 116, Log-Lik: -408970.671, Max-Change: 0.00191
Iteration: 117, Log-Lik: -408970.514, Max-Change: 0.00245
Iteration: 118, Log-Lik: -408970.216, Max-Change: 0.00305
Iteration: 119, Log-Lik: -408970.117, Max-Change: 0.00234
Iteration: 120, Log-Lik: -408970.047, Max-Change: 0.00453
Iteration: 121, Log-Lik: -408969.952, Max-Change: 0.00321
Iteration: 122, Log-Lik: -408969.881, Max-Change: 0.00432
Iteration: 123, Log-Lik: -408969.803, Max-Change: 0.00241
Iteration: 124, Log-Lik: -408969.720, Max-Change: 0.00381
Iteration: 125, Log-Lik: -408969.643, Max-Change: 0.00207
Iteration: 126, Log-Lik: -408969.581, Max-Change: 0.00118
Iteration: 127, Log-Lik: -408969.385, Max-Change: 0.00683
Iteration: 128, Log-Lik: -408969.287, Max-Change: 0.00108
Iteration: 129, Log-Lik: -408969.238, Max-Change: 0.00093
Iteration: 130, Log-Lik: -408969.077, Max-Change: 0.00116
Iteration: 131, Log-Lik: -408969.006, Max-Change: 0.00107
Iteration: 132, Log-Lik: -408968.946, Max-Change: 0.00115
Iteration: 133, Log-Lik: -408968.596, Max-Change: 0.00124
Iteration: 134, Log-Lik: -408968.538, Max-Change: 0.00126
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saveRDS(m1, "combined_irt_output/m1.rds")
m1 <-  readRDS("combined_irt_output/m1.rds")

Get factor scores

fscores <- fscores(m1, use_dentype_estimate=TRUE)[,1]
full2 <- data.frame(full)

##Confirmatory DETECT

dtct <- c(rep(1, 37), rep(2, 478))

conf <- conf.detect(full2, fscores, dtct)
## -----------------------------------------------------------
## Confirmatory DETECT Analysis 
## Conditioning on 1 Score
## Bandwidth Scale: 1.1 
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## -----------------------------------------------------------
##           unweighted weighted
## DETECT         0.098    0.098
## ASSI           0.069    0.069
## RATIO          0.245    0.245
## MADCOV100      0.400    0.400
## MCOV100        0.065    0.065

Does not seem like the 2-dimensional structure implied by the distinction between lexical items and grammatical items is justified.

Exploratory detect to look for any other form of multidimensionality.

d1 <- expl.detect(full2, fscores, nclusters=2)
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## 
## 
## DETECT (unweighted)
## 
## Optimal Cluster Size is  2  (Maximum of DETECT Index)
## 
##   N.Cluster N.items N.est N.val size.cluster DETECT.est ASSI.est RATIO.est
## 1         2     515  1093  1094      190-325      0.209    0.303     0.493
##   MADCOV100.est MCOV100.est DETECT.val ASSI.val RATIO.val MADCOV100.val
## 1         0.424       0.087      0.282    0.411     0.589         0.479
##   MCOV100.val
## 1        0.09

options(max.print=2000)
d1
## $detect.unweighted
##     DETECT.val  ASSI.val RATIO.val MADCOV100.val MCOV100.val
## Cl2  0.2820284 0.4106003 0.5889576     0.4788604  0.08960701
## 
## $detect.weighted
##     DETECT.val  ASSI.val RATIO.val MADCOV100.val MCOV100.val
## Cl2  0.2820284 0.4106003 0.5889576     0.4788604  0.08960701
## 
## $clusterfit
## 
## Call:
## stats::hclust(d = d, method = "ward.D")
## 
## Cluster method   : ward.D 
## Number of objects: 515 
## 
## 
## $itemcluster
##                     item cluster2
## 1          morphology761        1
## 2          morphology762        1
## 3          morphology763        1
## 4          morphology764        1
## 5          morphology765        1
## 6          morphology766        1
## 7          morphology767        1
## 8          morphology768        1
## 9          morphology769        1
## 10         morphology770        1
## 11         morphology771        1
## 12         morphology772        1
## 13             syntax773        1
## 14             syntax774        1
## 15             syntax775        1
## 16             syntax776        1
## 17             syntax777        1
## 18             syntax778        1
## 19             syntax779        1
## 20             syntax780        1
## 21             syntax781        1
## 22             syntax782        1
## 23             syntax783        1
## 24             syntax784        1
## 25             syntax785        1
## 26             syntax786        1
## 27             syntax787        1
## 28             syntax788        1
## 29             syntax789        1
## 30             syntax790        1
## 31             syntax791        1
## 32             syntax792        1
## 33             syntax793        1
## 34             syntax794        1
## 35             syntax795        1
## 36             syntax796        1
## 37             syntax797        1
## 38             alligator        2
## 39                animal        2
## 40                   ant        2
## 41                  bear        2
## 42                   bee        2
## 43                  bird        2
## 44                   bug        2
## 45                 bunny        2
## 46             butterfly        2
## 47                   cat        2
## 48      chicken..animal.        2
## 49                   cow        2
## 50                  deer        2
## 51                   dog        2
## 52                donkey        2
## 53                  duck        2
## 54              elephant        2
## 55         fish..animal.        2
## 56                  frog        2
## 57               giraffe        2
## 58                 goose        2
## 59                   hen        2
## 60                 horse        2
## 61                 kitty        2
## 62                  lamb        2
## 63                  lion        2
## 64                monkey        2
## 65                 moose        2
## 66                 mouse        2
## 67                   owl        2
## 68               penguin        2
## 69                   pig        2
## 70                  pony        2
## 71                 puppy        2
## 72               rooster        2
## 73                 sheep        2
## 74              squirrel        2
## 75             teddybear        2
## 76                 tiger        2
## 77                turkey        2
## 78                turtle        2
## 79                  wolf        2
## 80                 zebra        2
## 81              airplane        2
## 82               bicycle        2
## 83                  boat        2
## 84                   bus        2
## 85                   car        2
## 86             firetruck        2
## 87            helicopter        2
## 88            motorcycle        2
## 89                  sled        2
## 90              stroller        2
## 91               tractor        2
## 92                 train        2
## 93              tricycle        2
## 94                 truck        2
## 95                  ball        2
## 96               balloon        2
## 97                   bat        2
## 98                 block        2
## 99                  book        2
## 100              bubbles        2
## 101                chalk        2
## 102               crayon        2
## 103                 doll        2
## 104                 game        2
## 105                 glue        2
## 106                  pen        2
## 107               pencil        2
## 108           play.dough        2
## 109              present        2
## 110               puzzle        2
## 111                story        2
## 112         toy..object.        2
## 113                apple        2
## 114           applesauce        2
## 115               banana        2
## 116                beans        2
## 117                bread        2
## 118               butter        2
## 119                 cake        2
## 120                candy        2
## 121              carrots        2
## 122               cereal        2
## 123             cheerios        2
## 124               cheese        2
## 125       chicken..food.        2
## 126            chocolate        2
## 127               coffee        2
## 128                 coke        2
## 129               cookie        2
## 130                 corn        2
## 131              cracker        2
## 132                donut        2
## 133     drink..beverage.        2
## 134                  egg        2
## 135          fish..food.        2
## 136                 food        2
## 137         french.fries        2
## 138               grapes        2
## 139          green.beans        2
## 140                  gum        2
## 141            hamburger        2
## 142                  ice        2
## 143            ice.cream        2
## 144                jello        2
## 145                jelly        2
## 146                juice        2
## 147             lollipop        2
## 148                 meat        2
## 149                melon        2
## 150                 milk        2
## 151               muffin        2
## 152              noodles        2
## 153                 nuts        2
## 154        orange..food.        2
## 155              pancake        2
## 156                 peas        2
## 157        peanut.butter        2
## 158               pickle        2
## 159                pizza        2
## 160              popcorn        2
## 161             popsicle        2
## 162          potato.chip        2
## 163               potato        2
## 164              pretzel        2
## 165              pudding        2
## 166              pumpkin        2
## 167               raisin        2
## 168                 salt        2
## 169             sandwich        2
## 170                sauce        2
## 171             soda.pop        2
## 172                 soup        2
## 173            spaghetti        2
## 174           strawberry        2
## 175                toast        2
## 176                 tuna        2
## 177              vanilla        2
## 178             vitamins        2
## 179     water..beverage.        2
## 180               yogurt        2
## 181                beads        2
## 182                 belt        2
## 183                  bib        2
## 184                boots        2
## 185               button        2
## 186                 coat        2
## 187               diaper        2
## 188       dress..object.        2
## 189               gloves        2
## 190                  hat        2
## 191               jacket        2
## 192                jeans        2
## 193              mittens        2
## 194             necklace        2
## 195              pajamas        2
## 196                pants        2
## 197                scarf        2
## 198                shirt        2
## 199                 shoe        2
## 200               shorts        2
## 201              slipper        2
## 202              sneaker        2
## 203             snowsuit        2
## 204                 sock        2
## 205              sweater        2
## 206               tights        2
## 207           underpants        2
## 208               zipper        2
## 209                ankle        2
## 210                  arm        2
## 211         belly.button        2
## 212     buttocks.bottom.        2
## 213                cheek        2
## 214                 chin        2
## 215                  ear        2
## 216                  eye        2
## 217                 face        2
## 218               finger        2
## 219                 foot        2
## 220                 hair        2
## 221                 hand        2
## 222                 head        2
## 223                 knee        2
## 224                  leg        2
## 225                 lips        2
## 226                mouth        2
## 227                 nose        2
## 228         owie.boo.boo        1
## 229               penis.        2
## 230             shoulder        2
## 231                  toe        2
## 232               tongue        2
## 233                tooth        2
## 234                tummy        2
## 235              vagina.        2
## 236               basket        2
## 237              blanket        2
## 238               bottle        2
## 239                 bowl        2
## 240                  box        2
## 241                broom        2
## 242                brush        2
## 243               bucket        2
## 244               camera        2
## 245         can..object.        2
## 246                clock        2
## 247                 comb        2
## 248                  cup        2
## 249                 dish        2
## 250                 fork        2
## 251              garbage        2
## 252                glass        2
## 253              glasses        2
## 254               hammer        2
## 255                  jar        2
## 256                 keys        2
## 257                knife        2
## 258                 lamp        2
## 259                light        2
## 260             medicine        2
## 261                money        2
## 262                  mop        2
## 263                 nail        2
## 264               napkin        2
## 265                paper        2
## 266                penny        2
## 267              picture        2
## 268               pillow        2
## 269                plant        2
## 270                plate        2
## 271                purse        2
## 272                radio        2
## 273             scissors        2
## 274                 soap        2
## 275                spoon        2
## 276                 tape        2
## 277            telephone        2
## 278       tissue.kleenex        2
## 279           toothbrush        2
## 280                towel        2
## 281                trash        2
## 282                 tray        2
## 283               vacuum        2
## 284               walker        2
## 285       watch..object.        1
## 286             basement        2
## 287             bathroom        2
## 288              bathtub        2
## 289                  bed        2
## 290              bedroom        2
## 291                bench        2
## 292                chair        2
## 293               closet        2
## 294                couch        2
## 295                 crib        2
## 296                 door        2
## 297               drawer        2
## 298                dryer        2
## 299               garage        2
## 300           high.chair        2
## 301              kitchen        2
## 302          living.room        2
## 303                 oven        2
## 304             play.pen        2
## 305                porch        2
## 306                potty        2
## 307        rocking.chair        2
## 308         refrigerator        2
## 309                 room        2
## 310               shower        2
## 311                 sink        2
## 312                 sofa        2
## 313               stairs        2
## 314                stove        2
## 315                table        2
## 316                   TV        2
## 317               window        2
## 318      washing.machine        2
## 319             backyard        2
## 320                cloud        2
## 321                 flag        2
## 322               flower        2
## 323               garden        2
## 324                grass        2
## 325                 hose        2
## 326               ladder        2
## 327           lawn.mower        2
## 328                 moon        2
## 329                 pool        2
## 330                 rain        2
## 331                 rock        2
## 332                 roof        2
## 333              sandbox        2
## 334               shovel        2
## 335             sidewalk        2
## 336                  sky        2
## 337       slide..object.        2
## 338                 snow        2
## 339              snowman        2
## 340            sprinkler        2
## 341                 star        2
## 342                stick        2
## 343                stone        2
## 344               street        2
## 345                  sun        2
## 346       swing..object.        2
## 347                 tree        2
## 348 water..not.beverage.        2
## 349                 wind        2
## 350                 bite        1
## 351                 blow        1
## 352               break.        1
## 353                bring        1
## 354                build        1
## 355                 bump        1
## 356                  buy        1
## 357                carry        1
## 358                catch        1
## 359                chase        1
## 360                 clap        1
## 361       clean..action.        1
## 362                climb        1
## 363                close        1
## 364                 cook        1
## 365                cover        1
## 366                  cry        1
## 367                  cut        1
## 368                dance        1
## 369                 draw        1
## 370       drink..action.        2
## 371                drive        1
## 372                 drop        1
## 373         dry..action.        1
## 374                 dump        1
## 375                  eat        1
## 376                 fall        1
## 377                 feed        1
## 378                 find        1
## 379               finish        1
## 380                  fit        1
## 381                  fix        1
## 382                  get        1
## 383                 give        1
## 384                   go        1
## 385                 hate        1
## 386                 have        1
## 387                 hear        1
## 388                 help        1
## 389                 hide        1
## 390                  hit        1
## 391                 hold        1
## 392                  hug        1
## 393                hurry        1
## 394                 jump        1
## 395                 kick        1
## 396                 kiss        1
## 397                knock        1
## 398                 lick        1
## 399                 like        1
## 400               listen        1
## 401                 look        1
## 402                 love        1
## 403                 make        1
## 404                 open        1
## 405                paint        1
## 406                 pick        1
## 407                 play        1
## 408                 pour        1
## 409              pretend        1
## 410                 pull        1
## 411                 push        1
## 412                  put        1
## 413                 read        1
## 414                 ride        1
## 415                  rip        1
## 416                  run        1
## 417                  say        1
## 418                  see        1
## 419                shake        1
## 420                share        1
## 421                 show        1
## 422                 sing        1
## 423                  sit        1
## 424                skate        1
## 425                sleep        1
## 426       slide..action.        2
## 427                smile        1
## 428                spill        1
## 429               splash        1
## 430                stand        1
## 431                 stay        1
## 432                 stop        1
## 433                sweep        2
## 434                 swim        2
## 435       swing..action.        2
## 436                 take        1
## 437                 talk        1
## 438                taste        1
## 439                 tear        1
## 440                think        1
## 441                throw        1
## 442               tickle        1
## 443                touch        1
## 444                 wait        1
## 445                 wake        1
## 446                 walk        1
## 447                 wash        1
## 448       watch..action.        1
## 449                 wipe        1
## 450                 wish        1
## 451        work..action.        1
## 452                write        1
## 453             all.gone        1
## 454               asleep        1
## 455                awake        1
## 456                  bad        1
## 457               better        1
## 458                  big        1
## 459                black        2
## 460                 blue        2
## 461               broken        1
## 462                brown        2
## 463              careful        1
## 464  clean..description.        1
## 465                 cold        1
## 466                 cute        1
## 467                 dark        1
## 468                dirty        1
## 469    dry..description.        1
## 470                empty        1
## 471                 fast        1
## 472                 fine        1
## 473                first        1
## 474                 full        1
## 475               gentle        1
## 476                 good        1
## 477                green        2
## 478                happy        1
## 479                 hard        1
## 480                heavy        1
## 481                 high        1
## 482                  hot        1
## 483               hungry        1
## 484                 hurt        1
## 485                 last        1
## 486 little..description.        1
## 487                 long        1
## 488                 loud        1
## 489                  mad        1
## 490              naughty        2
## 491                  new        1
## 492                 nice        1
## 493                noisy        1
## 494                  old        1
## 495 orange..description.        2
## 496                 poor        1
## 497               pretty        1
## 498                quiet        1
## 499                  red        2
## 500                  sad        1
## 501               scared        1
## 502                 sick        1
## 503               sleepy        1
## 504                 slow        1
## 505                 soft        1
## 506               sticky        1
## 507                stuck        1
## 508              thirsty        1
## 509                 tiny        1
## 510                tired        1
## 511                  wet        1
## 512                white        2
## 513                windy        2
## 514               yellow        2
## 515                yucky        1
## 
## attr(,"class")
## [1] "expl.detect"

  1. This analysis considers all observations for which longitudinal==false. There are still many observations with the same values of original_id. Most of these appear to be participants who were tested at multiple time points as part of a data set that wasn’t exclusively longitudinal. However the help file for Wordbank indicates that this variable is not always reliable. We have therefore also run this analysis on a subset of these data withuut any duplicate original_ids)↩︎